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Preheat the oven to 350°. In a large bowl, whisk the flour with 1 teaspoon of salt. Using a pastry blender, cut in the butter until the mixture resembles coarse meal. Add the water and stir until a stiff dough forms.
Scrape the dough out onto a floured work surface and knead until smooth. If the dough is more than slightly tacky, knead in a few more tablespoons of flour. Shape the dough into a disk, wrap in plastic and refrigerate for 30 minutes.
On a floured work surface, cut the chilled dough into quarters. Cut each quarter into 3 equal pieces. Using a rolling pin, roll each piece into a ball, cover with plastic wrap and let rest for 15 minutes. Roll each ball into a very thin 7-inch tortilla.
Light a grill. Heat a cast-iron skillet. Lightly oil the skillet and cook each tortilla over moderately high heat until speckled with brown, about 1 minute per side. Transfer the tortilla to a large sheet of foil. Repeat with the remaining tortillas and wrap them in the foil.
Rub the steak with the olive oil and season with salt and pepper. Grill the steak over a medium-hot fire until medium rare, 12 to 14 minutes per side, depending on the thickness. Transfer the steak to a carving board and let rest for 10 minutes. Thinly slice the steak across the grain.
Heat the tortillas in the oven for about 5 minutes. Serve the steak and tortillas with the Pico de Gallo, Chunky Guacamole, Mango-Cucumber Salsa and Simple Black Beans.